1. Field of the Invention
The invention relates to an apparatus for determining the actual value of at least one of the stator resistance, the main inductance and the stray inductance parameters of an asynchronous machine having associated operating stator current and stator voltage vectors, from preset values of said parameters.
2. Description of the Prior Art
For the control of synchronous machines it is advantageous to set separate nominal values for the flux and the torque of the machine. One then obtains both a clear dynamic behavior easy to regulate and a high efficiency of the machine. For setting the desired flux, it must be possible to adjust the magnetizing component of the stator current, and for controlling the torque or the speed of rotation, the active component of the stator current, these two components being then combined to form the desired total stator current.
For the description of an asynchronous machine it is desirable to combine the currents flowing in the stator windings as a total stator current vector i of the magnitude i, and the stator voltages as a stator voltage vector u of the magnitude u. The magnetic field of the machine can be described by a flux vector, and the induced EMF by an EMF vector. In this discussion only the flux vector .PSI. (magnitude .psi.) in the rotor winding and the EMF vector e (magnitude e) in the rotor winding are considered for the description of flux and EMF of the machine. Only the component i.sub..phi.1 parallel to the flux vector .psi. contributes to the buildup of the magnetic field as magnetization current i.sub..mu., while the active current is given by the component i.sub.100 2 of the stator current perpendicular to the flux vector. The stator current vector i and stator voltage vector u can be tapped at the machine terminals and be described by the components in a stator-related (i.e. fixed) coordinate system, e.g. a Cartesian fixed coordinate system designated by the indices .alpha..sub.1 , .alpha..sub.2. With respect to the .alpha..sub.1 axis, the stator current has the angle .epsilon., the time derivative of which is given by the stator frequency .omega.. For the description of the asynchronous machine it is, however, advantageous to proceed from a field-oriented coordinate system which revolves with the flux vector .psi. and is given by an axis (index .phi..sub.1) parallel to the flux vector and an axis .phi..sub.2 perpendicular thereto. Accordingly, the field-oriented coordinate system is rotated relative to the stator reference system by an angle .phi. which is enclosed by the flux vector .psi. and the .alpha..sub.1 axis. For the above-mentioned field-oriented operation of a frequency converter-fed asynchronous machine, therefore, the nominal values of the stator current are set in the field-oriented reference system, from which the corresponding nominal values for the stator current vector to be set in the fixed stator reference system must be determined. This requires information about the relative position between field-oriented reference system and stator reference system (i.e. the angle .phi.).
The EMF vector e can be calculated from the stator-related coordinates (tapped on the machine) of the stator current vector i and of the stator voltage vector u according to the equation EQU e=u=i.multidot.r.sup.s -x.sup..sigma. .multidot.d/dt i (1)
By integration of this EMF vector the flux vector EQU .psi.=.intg.e dt (1a)
can be formed. Since for field-oriented control frequently only the information about the direction of the flux vector is needed, and since in the stationary case the flux vector and EMF vector are perpendicular to each other, one can perform instead of the integration a rotation of the EMF vector by 90.degree., or the direction of the EMF vector itself can be used. For the control as described e.g. in U.S. Pat. No. 3,824,437 (which corresponds to German Patent DE PS No. 19 41 312), therefore, any EMF former is required, in which the stator voltage vector and the stator current vector as well as the parameter values for the stator resistance r.sup.s and the stray inductance x.sup..sigma. are entered. The quality of this control depends on the exact setting of the parameters r.sup.s, x.sup..sigma..
In another method for flux determination one proceeds, not from the induced EMF, but from the processes leading to the formation of the field in the rotary field machine. In connection with this invention, the following relationships are important:
With the relationships illustrated in FIG. 1, the component, parallel to the flux vector .psi., of the stator current vector i is found to be EQU i.sub..phi.1 =i cos (.epsilon.-.phi.).
In the stationary case this component equals the magnetization current i.sub..mu. ; in dynamic states the magnetization current in the machine builds up with a time behavior which, using the Laplace operator S and the time constant T, can be written thus: EQU i.sub..mu. =i.sub..phi.1 1/1+ST (2)
The field produced in the rotor by this magnetization current is described by a flux vector EQU .psi.=i.sub..mu. .multidot.x.sup.h ( 3)
which induces in the rotor an EMF given by EQU e=d/dt.PSI. (3a)
In stationary form the differentiation can be represented by a rotation by 90.degree. and multiplication by the angular velocity .omega. of the stator current vector, so that we have for the vector magnitudes: EQU e=i.sub..mu. .multidot.x.sup.h .multidot..omega.
As the magnetization current i.sub..mu. is equal to the field-parallel stator current component i.sub..phi.1 only in the stationary case, this stator current component parallel to the flux vector .psi. is called the "magnetization current component." The parameter value for the main inductance x.sup.h of the machine is an important determining factor.
Since the parameters vary (e.g. r.sup.s due to thermal heating and x.sup.h due to saturation during operation of the asynchronous machine), it is necessary for an exact field-oriented control, to determine the parameter values belonging to the individual operation states.
Several proposals, not published with a prior date, have been made to use the two equations (1) and (3) for the determination of a parameter value, by calculating vector e or the respective flux vector .psi. in two ways which depend on the set parameter values. If one considers a determinant of the vectors calculated in different ways (e.g. the magnitude or a component parallel or perpendicular to the stator current) there results a difference between these determinants which depends on the accuracy of the parameter values used. By supplying this difference between the determinants to an integrating regulator and adjusting according to the regulator output signal the parameter value for the machine parameter to be determined, therefore, one can achieve, by balancing of the two vectors calculated in different ways, an adjustment of the parameter value used to the machine parameters to be determined.
In these non-predated proposals, the vector e or .psi. is determined in one instance according to equation (1) via an EMF former. The other method for the calculation of .psi. or e consists, according to one proposal, of an arithmetic model circuit which, on the basis of the actual machine currents and the rotor position as well as a variable parameter value for the rotor resistance, calculates a model flux vector or respectively a model EMF vector. Since the actual stator current vector is impressed on the computation model circuit, identical circle diagrams for .psi. or e apply, although the slip scaling is different if the parameter value of the rotor resistance differs from the machine rotor resistance. Although the arithmetic model circuit works with the actual rotor position, the model vector differs from the vector determined in the EMF former if the setting of the parameter value for the rotor resistance is imprecise. Now this deviation can be used for readjusting the parameter value used in the model to the machine parameter. In another proposal, the model vector is calculated in an arithmetic model circuit from the voltage vector and the rotor angle. In this case the actual voltage vector is impressed on the computation model, coincident circle diagrams for e or .psi. applying here also, which differ only in the slip scaling according to the incorrect setting of the rotor resistance parameter value. For determining the stator resistance, in both cases the fact can be used that the EMF vector component parallel to the stator current vector (active component) differs from the corresponding component of a vector formed from the stator voltage vector simply by subtraction of the inductive stray voltage, only by the ohmic stator voltage drop. If therefore one uses for the follow-up of the rotor resistance parameter as determining quantity for the EMF vector and the model EMF vector the component perpendicular to the stator current vector, after completed balance the reactive components of the vector determined in the EMF former and of the model vector will differ only by the product of stator current and stator resistance.
In both proposals, the rotor angle is required as actual value, but this is often difficult or even impossible to realize technically.